Questions
Can you play League of Legends with a controller on a Mac?
Not with any support from the game; League has never had controller input on any platform (Wild Rift, the mobile game, is the exception, and it is not on the Mac). What you can do is map a controller to the mouse and keys League uses with InputConfig, and play it as a mouse-and-keyboard player would. That is genuinely playable in normals and ARAM, and it is the way some people with limited hand use play at all. It is not going to win ranked.
The layout
Pointer on the left stick, with a slow-pointer chord for last hits. Right trigger to right-click, which is move and attack. Abilities Q, W, E, R on the face buttons, summoner spells on the bumpers, items on the D-pad and a chord, recall and shop on the stick clicks. The camera on the right stick as the edge-pan keys, or locked. The League of Legends layout in the app is this, ready to load.
What makes it work
Smart cast on every ability, so a button press casts at the pointer without a second click. Attack move on the trigger. Camera locked or on a stick, never on the mouse edge. Those three settings in League's options matter more than anything in the mapper.
What it will not do
A stick pointer is slower than a mouse for precise clicks, and League is a game of precise clicks. Expect to be slower at last-hitting and skillshots. For someone who cannot use a mouse, that trade is the whole point; for everyone else, it is a novelty or a sofa night.
Questions
Does League of Legends have controller support?
No, on any platform. A mapper such as InputConfig turns a controller into the mouse and keys it expects.
Is it bannable to play League with a controller mapper?
A mapper sends ordinary mouse and keyboard input, the same as any accessibility tool. It does not automate play.